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Sharpness overconstancy: the roles of visibility and current context
Vision Research 39 (1999) 2649 – 2657
Sharpness overconstancy: the roles of visibility and current context Susan J. Galvin *, Robert P. O’Shea, Abigail M. Squire, Diane S. Hailstone Department of Psychology, Uni6ersity of Otago, PO Box 56, Dunedin, New Zealand Received 24 June 1998; received in revised form 26 October 1998
Abstract In a previous study we found that blurred edges presented in peripheral vision look sharper than when they are looked at directly, a phenomenon we have called peripheral sharpness o6erconstancy (Galvin et al. (1997). Vision Research, 37, 2035–2039). In the current study we show that when visibility of the stimulus edges is compromised by very brief presentations, we can demonstrate sharpness overconstancy for static, foveal viewing. We also test whether the degree of sharpening is a function of the current visual context, but find no difference between the peripheral sharpness overconstancy (at 24° eccentricity) of edges measured in a blurred context and that measured in a sharp context. We conclude that if the visual system does carry a template for sharp edges which contributes to edge appearance when visibility is poor, then that template is resistant to changes in context. © 1999 Elsevier Science Ltd. All rights reserved. Keywords: Sharpness overconstancy; Edge blur; Visibility; Context; Appearance
1. Introduction We have been investigating the phenomenon that blurred edges sometimes look sharper than they really are. We encountered this effect in the course of considering a more general observation, namely, that the quality of the peripheral visual scene does not appear to degenerate away from the point of gaze. Although we are unable to perform certain tasks using peripheral vision, peripheral targets do not appear dim or blurry, and do not change their quality of appearance as the point of fixation changes. This can be considered a form of constancy: an object in the periphery is perceived veridically despite having a poorer quality retinal image than at the fovea, and having a degraded neural image produced by the first few steps of peripheral visual processing. In its efforts to maintain a consistent visual experience, however, the peripheral visual system actually seems to overcompensate for its reduced resolving power in the case of blurred edges, making them appear sharper when viewed peripherally than when viewed foveally, and producing an overconstancy. * Corresponding author. Fax: +64-3479-8335. E-mail address: [email protected] (S.J. Galvin)
Previously, we quantified the phenomenon of peripheral sharpness overconstancy (Galvin, O’Shea, Squire & Govan, 1997), and suggested that it may occur because the visual system relies on its knowledge of the world to help construct an appropriate percept in conditions of poor visibility. A default assumption of sharpness may have arisen because our visual world is dominated by sharp occlusion borders. The role of visibility in producing this effect was emphasised for us by an intriguing aspect of our original data, namely, that there was more sharpness overconstancy (that is, a bigger mismatch between the actual peripheral blur and the matched foveal blur) at greater eccentricities. We thought this consistent with our template theory because the visual system must rely more on default assumptions about objects the less visible they are. Because we had used the same field size at all eccentricities (4 × 4° squares) we could assume that our most peripheral stimuli were the least visible because their perception would have engaged the least cortical machinery. In Experiment 2 of that first study, we equated visibility across eccentricities by increasing the stimulus size according to a cortical magnification factor based on the number of retinal ganglion cells leaving the different regions of the retina (Rovamo & Virsu, 1979). This made the eccentricity effect disappear; the observ-
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ers matched a particular blur to the same (sharper) foveal blur at all the eccentricities we tested. Another form of sharpness overconstancy can occur when we view moving objects. Not only does the visual system compensate for the one-dimensional smearing of motion blur (Burr, 1980), it also sharpens moving, blurred stimuli (Ramachandran, Rao & Vidyasagar, 1974; Prather & Ramachandran, 1991; Bex, Edgar & Smith, 1995; Hammett & Bex, 1996). Moving a blurred edge decreases its visibility, increasing blur discrimination thresholds (Pa¨a¨kko¨nen & Morgan, 1994), so this is another example of the appearance of an edge tending towards sharpness as its visibility is decreased. In this paper we examine whether sharpness overconstancy is just a special property of peripheral vision and motion perception, or if it can occur under other conditions of poor visibility. We predicted that if a blurred edge is presented very briefly to the fovea, and the observer then reports its sharpness, then the stimuli presented most briefly will be the hardest to see, and will give the most sharpness overconstancy. In Experiment 1 we have measured apparent blur for a range of stimulus durations less than 1 s. We have assumed that the default assumption of sharpness is due, at least in part, to years of experience with sharp edges in the world seen foveally. We were interested to know how much contribution, if any, is made to peripheral sharpness overconstancy by the currently visible scene outside the stimulus field. We hypothesised that measuring blur appearance within a blurry context would cause the visual system to modify its assumption regarding the sharpness of things in the periphery, and yield reduced overconstancy. We have put this idea to the test in Experiment 2.
about 13 arc min, discrimination thresholds are higher for 40 ms presentations than for 150 ms presentations. Presenting blurred edges for very short periods therefore reduces their visibility, and so we predict that decreasing stimulus durations will also increase edge sharpening.
2.2. Method Three experienced observers, aged between 23 and 43, with normal or corrected-to-normal vision, voluntarily participated in the experiment. Stimuli were high contrast edges presented on a monochrome 12-inch monitor (Apple model MO400). The blurred edges had cumulative Gaussian luminance profiles,9 3 standard deviations in extent. We used 11 standard deviations ranging from 0 to 20 arc min, giving a range of blur extents from 0 to 2°. The observers viewed these foveally, with the left eye. Test edges were presented for one of seven durations (17, 33, 67, 133, 267, 533, or 1067 ms). Each observation interval was followed 1 s later by an edge with an adjustable blur, which the observers used to report how blurry the briefly presented edge had appeared. This adjustable blur could range between 0 and 20 arc min, in 2 min steps. The observers were asked to match the blur extent of the test blur, and to ignore any apparent change in the contrast of the edge. The position of the middle of the edge with respect to the fixation target was jittered randomly over a range of9 1° from trial to trial. This prevented the observer using the apparent size of the black or white regions of the stimulus to determine the blur extent.
2.3. Results and discussion 2. Experiment 1
2.1. Fo6eal sharpness o6erconstancy with short stimulus durations The claim that presenting something very briefly makes it harder to see has good face validity—we experience this while driving, when the demands of safety require that we get only a quick look at some interesting object off the road, and we resort to interrogating our passengers about its details. We can operationally define conditions of poor visibility as being those under which psychophysical performance in some relevant task is poor. The visibility of blurred edges can be assessed by their blur discrimination thresholds. Westheimer (1991) showed that as stimulus durations dropped below 130 ms, more blur was required to make a blurred edge discriminable from a sharp one. Burr and Morgan (1997) have shown that for Gaussian blurred edges with space constants ranging from 0 to
The responses of our three observers were very similar, so we have presented their average blur matches for eight stimulus durations in Fig. 1. The diagonal line shows where the data would have lain if the edges had been seen veridically; data falling below this line indicate blur matches that are sharper than the true blur of the edges. Straight lines fitted to the eight functions yielded slopes significantly less than 1.0 for exposure durations of half a second or less. These slopes are plotted in Fig. 2, and can be seen to increase quickly over the first 150 ms, then slowly to approach 1.0. The absolute size of the sharpness overconstancy, given by the vertical distance between any datum and the constancy line, increased as the stimulus duration decreased. This supported our notion that the sharp template is applied when the stimulus is hard to see. Sharpness overconstancy is greater for bigger blurs, as it is for all but the smallest blurred edges viewed in the periphery (Galvin et al., 1997).
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Fig. 1. Matched blurs as a function of stimulus blur, for seven stimulus durations. The diagonal line shows where the means should fall for perfect sharpness constancy. Each data point is the mean of four trials from each of the three observers. The bars show standard errors.
Because the very short stimulus durations precluded eye movements, it might be argued that the sharpening of some of the edges was a peripheral sharpening effect rather than arising from the brief presentations. (Recall that we randomly jittered the positions of the edge over a9 1° range.) We think this unlikely as there was a gradation in the amount of sharpening for stimulus durations of 133 ms or less, yet none of these would have allowed for the completion of an eye-movement during the stimulus presentation. A multiple regression of the matches against stimulus blur extent and stimulus blur position showed no systematic variation of performance with edge position, except for one observer, in whom edge position accounted for 2% of the variance. We ran this subject again with all the stimulus edges centred in their fields. Under these conditions, the overconstancy effect was much reduced, and the ob-
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server reported being unable to resist relying on the size of the black and white areas rather than edge blur to make matches. Nevertheless, there was still a significant difference between the slopes of the regression lines for the longest and shortest duration stimuli, showing that the overconstancy due to viewing the stimulus only briefly can survive the strong cue for a true match provided by the size of the uniform regions of the stimulus. Our observers reported no blurring of sharp edges, even at our shortest durations. Other researchers have reported an increase in the apparent blur of very small blurs for short durations similar to those used in the current study (Westheimer, 1991; Lacassagne, O8 gmen & Bedell, 1996; Burr & Morgan, 1997). Our study was not designed to pay particular attention to small blurs, and our measurement tool may not have had the resolution to reveal a slight apparent blurring of sharp edges. We consider the appearances of very small blurs in the general discussion. Westheimer (1991) speculated that blur detection thresholds in his observers got larger at short durations because the effective contrast of his stimuli was reduced; reducing contrast is known to increase blur detection thresholds (Hamerly & Dvorak, 1981). A simple reduction in the effective contrast of the edge would make the apparent luminance gradient shallower, and might cause the edge to look blurrier. It could also make the margins of the blur extent indistinguishable from the areas of uniform illumination, which could either make the blurred region appear to be narrower or wider, depending on whether the indistinguishable region was perceived as belonging to the uniform areas or to the blur itself. Although a reduction in effective contrast may produce uncertainty about the stimulus, this does not explain why the edge is seen as being sharper than it is, rather than more blurred. We suggest that in the absence of a clear interpretation of the information in the stimulus, this ambiguity might be resolved by reference to a high-level template for sharpness. We tested one consequence of this idea in Experiment 2.
3. Experiment 2
3.1. Peripheral sharpness o6erconstancy in blurry and sharp contexts
Fig. 2. Slopes of the regression lines fitted to the data in Fig. 1. The bars show standard errors.
The aim of this experiment was to discover if presenting blurred edges in a blurry context would reduce the sharpness of the default assumption about edges, and reduce the size of the peripheral sharpness overconstancy effect.
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Fig. 3 (A). Caption opposite.
3.2. Method A bird’s-eye view of the experimental setup is shown in Fig. 3(A). We constructed a large screen to serve as a projection surface for the background patterns. A sheet of draughting paper 2 m high and 3 m wide was bent into a half cylinder with a vertical axis, and a radius of 1 m. The observer sat with his or her head at the centre of this cylinder, and the screen filled all of the left, right, and superior regions of the observer’s visual field, and most of the inferior field. Stimulus edges were presented at two locations on the screen, both at eye-height, using two slide projectors positioned just behind the observer’s shoulders. The observer fixated one projected edge in the middle of the screen, while the other edge was presented 24° to the right of the foveal stimulus. There were two experimental conditions: in the sharp condition, a pattern of broad (6°), sharp-edged, wiggly lines was projected onto the back of the screen using two overhead projectors. The contrast of this pattern was 85%. In the blurry condition, the same pattern was projected but was Gaussian-blurred. The right side of the visual scene, as seen by the observer in the blurry condition, is shown in Fig. 3(B). The edges of the blurred lines in the wiggly-line pattern were measured
with a custom-built microphotometer with an aperture of 1.4 arc min, and were shown to have blur extents of 5°. In both conditions, the scene was produced by two overhead transparencies, and a thick paper border was fixed to each so light from one projector would not impinge on the region of the screen served by the other projector. The patterns cast by the two projectors came together on the screen in a dark vertical line (see the left edge of Fig. 3B), and this seam was positioned approximately 15° to the left of the foveal stimulus field. The luminance of the background images varied between 30 and 300 cd m − 2, and the projector serving the side of the screen carrying the stimuli was angled so that the point of maximum luminance measured from the observer’s eye was half way between the two stimulus fields. In both conditions, two dark patches on the overhead transparencies produced dark squares on the screen subtending 10×10°. These blocking squares were centred on the two 5×5° stimulus fields, so minimal luminance was added to the stimulus regions by the overhead projectors. The borders of the blocking squares were sharp on the screen in the sharp condition, but optically blurred in the blurry condition. The blur extent of the edges of the blocking squares in the blurry condition was 1°.
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Fig. 3(B) Fig. 3. (A) Apparatus for presenting blurred edges in blurry and sharp contexts. Two transparencies carrying the background patterns were projected onto the outside of an upright half-cylinder of drafting paper, 2 m tall and 1 m in diameter. The left (foveal) and right (24° eccentric) stimulus slides were projected over the shoulders of the observer, who sat with the observing eye on the axis of the cylinder. (B) Right side of the screen in Experiment 2 from the point of view of the observer, in the blurred condition. The wavy background pattern was blurred using Adobe Photoshop. The background pattern and the 10× 10° black blocking squares surrounding the stimulus field were then optically blurred. The blurred borders of the 5 ×5° stimulus field were produced by a small square window in the optical path within each slide projector. The observer fixated the centre of the left stimulus field.
The stimuli were slides of computer-generated, horizontal, Gaussian-blurred edges. We used the method of constant stimuli, presenting one of three standard edges in the periphery, with blur extents of 1.2, 1.6, or 2.0°. Each standard was judged against a set of eight foveal comparison blurs. The extents of the
comparison blurs increased in steps of 0.2°, and the range of comparison blurs for each standard blur was centred on that standard. The edges were centred in 5× 5° fields. The foveal and peripheral edges had Michelson contrasts of 0.91 and 0.94, respectively.
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We applied a rectangular window of black duct tape directly to a glass heat shield in the optical path of each slide projector, producing blurred borders for the stimulus fields. These edges had a blur extent of 0.8° on the screen. The borders of the stimulus fields were blurred in this way for both the blurred and sharp conditions. We wanted borders in the immediate vicinity of the test edges to be the same in both conditions as we were interested in the effect of changing the blur content of the global visual scene, and were not attempting to measure local induction effects. Observers performed a two-spatial-interval forcedchoice task. On each trial, one of the three peripheral standards was paired with one of its eight comparison blurs presented foveally, and the observer had to indicate which one was blurrier. The observer was asked to make this judgement on the basis of the apparent blur extent, and not the apparent contrast of the blur. Decision time was not restricted, but was not usually more than 2 s. Responses were recorded by hand by the experimenter, who also advanced the slides. The eight trials for each of the three standards were randomly interleaved in each block. These 24 trials were followed by the presentation of two black slides, then the 24 pairs of slides were presented again in the reverse order. Each observer ran ten of these 48-trial blocks in each condition. The order of the conditions was swapped each session. We constructed a separate 8-point psychometric function for each standard, each datum based on 20 trials. From these we derived a point of subjective equality (PSE) for each standard, that is, the foveal blur that would be judged blurrier or sharper than the standard equally often. Three observers voluntarily participated, aged 23 to 36, all members of the vision group at the University of Otago. SG and EW are mildly myopic, with corrections of less than 2 dioptres. DG is emmetropic. All observations were made with vision corrected to normal. EW was naı¨ve about the aims of the experiment.
Fig. 4 (filled symbols). All observers showed small overconstancy effects for all three standard peripheral blurs, with the exception of SG, whose overconstancy for the 2.0° standard was less than significant in both conditions. The foveal matches for the three standard blurs were not significantly different in the blurry and sharp background conditions for any of the observers. We noticed that the amount of overconstancy measured in this experimental setup was rather less than that obtained using the method of adjustment with blurred edges presented on computer monitors. We thought that one reason for this might be that the positions of the peripheral standard edges were not varied, allowing the observer to use the size of the light region of the stimulus to judge the size of the blur extent, bringing the observer’s PSEs closer to the con-
3.3. Results and discussion Each psychometric function was fit with a logistic distribution function, y =100/(1 +exp (− (x − m)/u)), where y is the percentage of responses ‘foveal sharper than peripheral’, x is the blur extent of the comparison blurs, and u is the slope parameter. The parameter m was taken as our estimate of the PSE, as it defines the point on the stimulus axis which gives the y value as 0.5. The standard error for this parameter was multiplied by 1.96 to give 95% confidence intervals for each PSE. The R 2 values for the fits of logistic functions for all observers had a mean of 0.957, and ranged from 0.902 to 0.997. The PSEs obtained in this way for three observers are plotted against the blur of the peripheral standards in
Fig. 4. Points of subjective equality (PSEs) for three peripheral blurs, presented at 24° eccentricity, in the blurred (round symbols) and sharp (square symbols) conditions, for three observers. The diagonal line in each graph indicates perfect sharpness constancy. Filled symbols show data measured with all the stimulus edges centred in their square fields. For two observers, results are also shown (open symbols) for measurements taken with the positions of the peripheral standard edges jittered over the range 91°. Error bars show 95% confidence intervals.
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stancy line. Observer SG reported that this cue was most distracting for the largest blurs, which might explain why her overconstancy effect decreased with increasing standard blur, rather than increased, as seen in the results from EW and DG, and in the studies reported in Galvin et al. (1997). We jittered the vertical positions of the edges in six steps over9 1°, and repeated the experiment with two observers. Their PSEs are plotted with open symbols in Fig. 4. It can be seen that jittering the position of the edges significantly increased SG’s overconstancy for the two larger standard blurs, producing the familiar pattern of increasing overconstancy with increasing standard blur. Jittering the edge positions produced no significant change in overconstancy in DG, who already showed the expected increase in sharpness overconstancy with blur extent with non-jittered stimuli. Most importantly, both observers continued to show no difference in sharpness overconstancy measured in blurry and sharp contexts. We have proposed that subjective edge sharpening is a high-level effect brought about by our knowledge of typical properties of the visual scene. If this is true, then sharpening might be affected not only by properties of the edge itself, but also by a manipulation of the global visual scene. We made what we thought would be a relevant and radical change, blurring everything in the scene surrounding the edge. This produced no change in the sharpness overconstancy in our observers, so we conclude that the template, if it exists, is not affected by the broad context in which an edge is presented.
4. General discussion We have shown that presenting blurred edges for short durations produces sharpness overconstancy for foveal viewing. Recently, Hammett and Georgeson (1998) measured the apparent sharpness of blurred square waves and also found that apparent sharpness increased with decreasing stimulus duration. We have argued that these findings are consistent with the theory that sharpness overconstancy manifests itself under conditions of poor visibility, as it is these conditions which force us to rely on our knowledge of the world as dominated by sharp luminance transitions. We have claimed that, in general, manipulations that increase blur discrimination thresholds also increase sharpening. An exception to this, which we have noted previously (Hailstone, 1997; Galvin, Squire, Hailstone & O’Shea, 1998b), is that plots of just-noticeable differences (JNDs) in blur against pedestal blur exhibit a dipper shape for small blurs, in both fovea and periphery (Hess, Pointer, & Watt, 1989), but we have found only monotonic increases in blur appearance with increases in real blur in peripheral vision. Dipper-shaped blur threshold functions have been modelled by
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Pa¨a¨kko¨nen and Morgan (1994), who apply Weber’s Law to an internal representation of blur which takes into account the effects of intrinsic blur. This model implies that the internal JNDs in blur increase monotonically with pedestal blur, even for the smallest blurs, and it may be these JNDs to which changes in appearance are related. We agree that the appearance of edges may be affected by intrinsic blur, as we (Galvin et al., 1997) found a slight blurring of sharp edges in peripheral vision which matched estimates of intrinsic blur made by Levi and Klein (1990). There is disagreement in the literature about the nature of the relationship between blur thresholds and blur appearance. Hammett (1997) argued that, in the case of moving, blurred edges, it is the motion sharpening process itself that produces increases in the blur discrimination thresholds. He based this conclusion on the finding that it was blurred edges moving at different (slow) speeds, but with the same apparent extents, that had the same Weber fractions for blur discrimination, rather than blurs that had the same physical extents. Burr and Morgan (1997), on the other hand, proposed that the appearance and discrimination of moving stimuli may be determined by different mechanisms, finding a much larger effect of increasing exposure duration from 40 to 150 ms on the apparent length of the smear tail of moving dots than on blur discrimination thresholds. It is unclear whether a single model will eventually account for the changes in both blur discrimination and blur appearance that occur when visibility is compromised in various ways; existing models of blur discrimination have not attempted to explain the appearance of briefly presented blurs. We rejected a number of low-level explanations for sharpness overconstancy in a previous paper (Galvin et al., 1997) but were impressed by the findings of Hammett and Bex (1996). They showed that sharpening of a drifting sinusoid could be reduced by adapting to stimuli containing higher spatial frequencies than the test stimulus, and suggested that some low-level non-linearity in contrast coding could be generating spatial frequencies higher than that of the test, which would in turn produce a sharper percept. Recently, Hammett, Georgeson and Gorea (1998) have developed this idea into a model which explains the motion sharpening as a result of compressive contrast non-linearities in ganglion cells of the magnocellular pathway (M cells). Fits of their model show that the degree of compression in the non-linearity required to produce their empirical shifts in blur appearance are consistent with those recorded in individual M cells. They argue that both kinds of sharpness overconstancy for static stimuli have been measured in conditions where M cells make a large contribution to perception: the perception of short duration stimuli is mediated by the transient subcortical system, and the peripheral sharpness overconstancy
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effect is accounted for by the higher ratio of M to P cells in the periphery. Although we find the argument that a contrast nonlinearity could produce sharpness overconstancy compelling, we are cautious about assigning this effect to the M pathways. Lennie (1993) and others (e.g. Merigan, Byrne & Maunsell, 1991; Galvin, Williams & Coletta, 1996) have argued that the P cell population can contribute significantly to the representation of transient and moving stimuli. Parvocellular neurons of the lateral geniculate nucleus have a peak temporal sensitivity of 10 Hz in monkeys (Derrington & Lennie, 1984), so we would predict that neurons in the human visual system should prefer a 100 ms stimulus, yet we found significant sharpness overconstancy with a similar duration in Experiment 1. A more specific objection to Hammett’s intriguing suggestion is that if compressive non-linearity in contrast coding by M cells accounted for sharpening in the short duration case, it does not explain why equating for visibility by M-scaling stimulus field sizes in the peripheral study equates overconstancy (Galvin et al., 1997), as changing the field size does not change the ratio of M to P cells. Another explanation for apparent sharpening of blurred edges was offered by Burr and Morgan (1997). They suggested that blur appearance is determined by a default rule that the blur looks like the sharpest blur from which it cannot be distinguished. We have compared the sharpening measured in the current study with the most appropriate available blur discrimination data, those for the 95% contrast, stationary, short-duration bars reported in Burr and Morgan (1997), and find that over most of the range of blurs we have examined (that is, all but the very small ones), the shifts in blur appearance are much larger than the JNDs for the same blurs, so poor blur discrimination does not fully account for the sharpening effect. We have found the same to be true for blurs presented in the periphery, where sharpness overconstancy exceeded blur decrement thresholds for blurs with space constants of 12 to 20 arc min (Hailstone, 1997). We have offered the idea of a sharpness template in the spirit of a Gestalt-like principle which might be derived from Wertheimer’s Law of Pra¨gnanz, which suggests that our perceptions will make good order out of incoming information (Koffka, 1935). We wondered if such a high-level mechanism might be susceptible to a global change in the visual scene, and tried to recalibrate our observers’ assumptions about the nature of typical luminance transitions by measuring blur appearance in a totally blurry context. We found that blurring the current visual context plays no role in defining the default assumption about the blurriness of the world. This may mean that there is no template for sharp edges to be influenced, or it may be that the template is very robust, perhaps yielding only to a prolonged pe-
riod of adaptation to blur. Myopes who are accustomed to enduring a blurry scene for the duration of the occasional search for their spectacles may have been conditioned out of adjusting their edge templates; our observers were emmetropic or near-emmetropic, and showed a similar resistance to any effect of a blurred context on edge appearance.
5. Conclusion Blurred edges presented for durations of less than 1 s undergo sharpening. This new observation complements measurements of peripheral sharpness overconstancy and motion sharpening, providing a third demonstration of sharpness overconstancy in conditions of poor visibility. We have argued that these results are consistent with the idea that our perception of edges is influenced by a template for edges that is sharp. We have found no effect of a completely blurry context on measurements of peripheral sharpness overconstancy, and conclude that if there is a template for edges, it is resistant to contextual influences.
Acknowledgements We would like to thank Donovan Govan, James Dignan, and Carl Beuke for being experimenters, Donovan Govan and Emma Willcock for being observers, and Donovan Govan for programming and scene measurement. We thank Jeff Miller for suggesting Experiment 1. We thank David Burr and an anonymous reviewer for helpful comments on the original manuscript. Some of the data in this study were presented at ICONIP’97 (Galvin et al., 1998b) and the 1998 meeting of the Association for Research in Vision and Ophthalmology (Galvin, Squire, Hailstone, & O’Shea, 1998a).
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Sharpness overconstancy: the roles of visibility and current context Susan J. Galvin *, Robert P. O’Shea, Abigail M. Squire, Diane S. Hailstone Department of Psychology, Uni6ersity of Otago, PO Box 56, Dunedin, New Zealand Received 24 June 1998; received in revised form 26 October 1998
Abstract In a previous study we found that blurred edges presented in peripheral vision look sharper than when they are looked at directly, a phenomenon we have called peripheral sharpness o6erconstancy (Galvin et al. (1997). Vision Research, 37, 2035–2039). In the current study we show that when visibility of the stimulus edges is compromised by very brief presentations, we can demonstrate sharpness overconstancy for static, foveal viewing. We also test whether the degree of sharpening is a function of the current visual context, but find no difference between the peripheral sharpness overconstancy (at 24° eccentricity) of edges measured in a blurred context and that measured in a sharp context. We conclude that if the visual system does carry a template for sharp edges which contributes to edge appearance when visibility is poor, then that template is resistant to changes in context. © 1999 Elsevier Science Ltd. All rights reserved. Keywords: Sharpness overconstancy; Edge blur; Visibility; Context; Appearance
1. Introduction We have been investigating the phenomenon that blurred edges sometimes look sharper than they really are. We encountered this effect in the course of considering a more general observation, namely, that the quality of the peripheral visual scene does not appear to degenerate away from the point of gaze. Although we are unable to perform certain tasks using peripheral vision, peripheral targets do not appear dim or blurry, and do not change their quality of appearance as the point of fixation changes. This can be considered a form of constancy: an object in the periphery is perceived veridically despite having a poorer quality retinal image than at the fovea, and having a degraded neural image produced by the first few steps of peripheral visual processing. In its efforts to maintain a consistent visual experience, however, the peripheral visual system actually seems to overcompensate for its reduced resolving power in the case of blurred edges, making them appear sharper when viewed peripherally than when viewed foveally, and producing an overconstancy. * Corresponding author. Fax: +64-3479-8335. E-mail address: [email protected] (S.J. Galvin)
Previously, we quantified the phenomenon of peripheral sharpness overconstancy (Galvin, O’Shea, Squire & Govan, 1997), and suggested that it may occur because the visual system relies on its knowledge of the world to help construct an appropriate percept in conditions of poor visibility. A default assumption of sharpness may have arisen because our visual world is dominated by sharp occlusion borders. The role of visibility in producing this effect was emphasised for us by an intriguing aspect of our original data, namely, that there was more sharpness overconstancy (that is, a bigger mismatch between the actual peripheral blur and the matched foveal blur) at greater eccentricities. We thought this consistent with our template theory because the visual system must rely more on default assumptions about objects the less visible they are. Because we had used the same field size at all eccentricities (4 × 4° squares) we could assume that our most peripheral stimuli were the least visible because their perception would have engaged the least cortical machinery. In Experiment 2 of that first study, we equated visibility across eccentricities by increasing the stimulus size according to a cortical magnification factor based on the number of retinal ganglion cells leaving the different regions of the retina (Rovamo & Virsu, 1979). This made the eccentricity effect disappear; the observ-
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ers matched a particular blur to the same (sharper) foveal blur at all the eccentricities we tested. Another form of sharpness overconstancy can occur when we view moving objects. Not only does the visual system compensate for the one-dimensional smearing of motion blur (Burr, 1980), it also sharpens moving, blurred stimuli (Ramachandran, Rao & Vidyasagar, 1974; Prather & Ramachandran, 1991; Bex, Edgar & Smith, 1995; Hammett & Bex, 1996). Moving a blurred edge decreases its visibility, increasing blur discrimination thresholds (Pa¨a¨kko¨nen & Morgan, 1994), so this is another example of the appearance of an edge tending towards sharpness as its visibility is decreased. In this paper we examine whether sharpness overconstancy is just a special property of peripheral vision and motion perception, or if it can occur under other conditions of poor visibility. We predicted that if a blurred edge is presented very briefly to the fovea, and the observer then reports its sharpness, then the stimuli presented most briefly will be the hardest to see, and will give the most sharpness overconstancy. In Experiment 1 we have measured apparent blur for a range of stimulus durations less than 1 s. We have assumed that the default assumption of sharpness is due, at least in part, to years of experience with sharp edges in the world seen foveally. We were interested to know how much contribution, if any, is made to peripheral sharpness overconstancy by the currently visible scene outside the stimulus field. We hypothesised that measuring blur appearance within a blurry context would cause the visual system to modify its assumption regarding the sharpness of things in the periphery, and yield reduced overconstancy. We have put this idea to the test in Experiment 2.
about 13 arc min, discrimination thresholds are higher for 40 ms presentations than for 150 ms presentations. Presenting blurred edges for very short periods therefore reduces their visibility, and so we predict that decreasing stimulus durations will also increase edge sharpening.
2.2. Method Three experienced observers, aged between 23 and 43, with normal or corrected-to-normal vision, voluntarily participated in the experiment. Stimuli were high contrast edges presented on a monochrome 12-inch monitor (Apple model MO400). The blurred edges had cumulative Gaussian luminance profiles,9 3 standard deviations in extent. We used 11 standard deviations ranging from 0 to 20 arc min, giving a range of blur extents from 0 to 2°. The observers viewed these foveally, with the left eye. Test edges were presented for one of seven durations (17, 33, 67, 133, 267, 533, or 1067 ms). Each observation interval was followed 1 s later by an edge with an adjustable blur, which the observers used to report how blurry the briefly presented edge had appeared. This adjustable blur could range between 0 and 20 arc min, in 2 min steps. The observers were asked to match the blur extent of the test blur, and to ignore any apparent change in the contrast of the edge. The position of the middle of the edge with respect to the fixation target was jittered randomly over a range of9 1° from trial to trial. This prevented the observer using the apparent size of the black or white regions of the stimulus to determine the blur extent.
2.3. Results and discussion 2. Experiment 1
2.1. Fo6eal sharpness o6erconstancy with short stimulus durations The claim that presenting something very briefly makes it harder to see has good face validity—we experience this while driving, when the demands of safety require that we get only a quick look at some interesting object off the road, and we resort to interrogating our passengers about its details. We can operationally define conditions of poor visibility as being those under which psychophysical performance in some relevant task is poor. The visibility of blurred edges can be assessed by their blur discrimination thresholds. Westheimer (1991) showed that as stimulus durations dropped below 130 ms, more blur was required to make a blurred edge discriminable from a sharp one. Burr and Morgan (1997) have shown that for Gaussian blurred edges with space constants ranging from 0 to
The responses of our three observers were very similar, so we have presented their average blur matches for eight stimulus durations in Fig. 1. The diagonal line shows where the data would have lain if the edges had been seen veridically; data falling below this line indicate blur matches that are sharper than the true blur of the edges. Straight lines fitted to the eight functions yielded slopes significantly less than 1.0 for exposure durations of half a second or less. These slopes are plotted in Fig. 2, and can be seen to increase quickly over the first 150 ms, then slowly to approach 1.0. The absolute size of the sharpness overconstancy, given by the vertical distance between any datum and the constancy line, increased as the stimulus duration decreased. This supported our notion that the sharp template is applied when the stimulus is hard to see. Sharpness overconstancy is greater for bigger blurs, as it is for all but the smallest blurred edges viewed in the periphery (Galvin et al., 1997).
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Fig. 1. Matched blurs as a function of stimulus blur, for seven stimulus durations. The diagonal line shows where the means should fall for perfect sharpness constancy. Each data point is the mean of four trials from each of the three observers. The bars show standard errors.
Because the very short stimulus durations precluded eye movements, it might be argued that the sharpening of some of the edges was a peripheral sharpening effect rather than arising from the brief presentations. (Recall that we randomly jittered the positions of the edge over a9 1° range.) We think this unlikely as there was a gradation in the amount of sharpening for stimulus durations of 133 ms or less, yet none of these would have allowed for the completion of an eye-movement during the stimulus presentation. A multiple regression of the matches against stimulus blur extent and stimulus blur position showed no systematic variation of performance with edge position, except for one observer, in whom edge position accounted for 2% of the variance. We ran this subject again with all the stimulus edges centred in their fields. Under these conditions, the overconstancy effect was much reduced, and the ob-
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server reported being unable to resist relying on the size of the black and white areas rather than edge blur to make matches. Nevertheless, there was still a significant difference between the slopes of the regression lines for the longest and shortest duration stimuli, showing that the overconstancy due to viewing the stimulus only briefly can survive the strong cue for a true match provided by the size of the uniform regions of the stimulus. Our observers reported no blurring of sharp edges, even at our shortest durations. Other researchers have reported an increase in the apparent blur of very small blurs for short durations similar to those used in the current study (Westheimer, 1991; Lacassagne, O8 gmen & Bedell, 1996; Burr & Morgan, 1997). Our study was not designed to pay particular attention to small blurs, and our measurement tool may not have had the resolution to reveal a slight apparent blurring of sharp edges. We consider the appearances of very small blurs in the general discussion. Westheimer (1991) speculated that blur detection thresholds in his observers got larger at short durations because the effective contrast of his stimuli was reduced; reducing contrast is known to increase blur detection thresholds (Hamerly & Dvorak, 1981). A simple reduction in the effective contrast of the edge would make the apparent luminance gradient shallower, and might cause the edge to look blurrier. It could also make the margins of the blur extent indistinguishable from the areas of uniform illumination, which could either make the blurred region appear to be narrower or wider, depending on whether the indistinguishable region was perceived as belonging to the uniform areas or to the blur itself. Although a reduction in effective contrast may produce uncertainty about the stimulus, this does not explain why the edge is seen as being sharper than it is, rather than more blurred. We suggest that in the absence of a clear interpretation of the information in the stimulus, this ambiguity might be resolved by reference to a high-level template for sharpness. We tested one consequence of this idea in Experiment 2.
3. Experiment 2
3.1. Peripheral sharpness o6erconstancy in blurry and sharp contexts
Fig. 2. Slopes of the regression lines fitted to the data in Fig. 1. The bars show standard errors.
The aim of this experiment was to discover if presenting blurred edges in a blurry context would reduce the sharpness of the default assumption about edges, and reduce the size of the peripheral sharpness overconstancy effect.
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Fig. 3 (A). Caption opposite.
3.2. Method A bird’s-eye view of the experimental setup is shown in Fig. 3(A). We constructed a large screen to serve as a projection surface for the background patterns. A sheet of draughting paper 2 m high and 3 m wide was bent into a half cylinder with a vertical axis, and a radius of 1 m. The observer sat with his or her head at the centre of this cylinder, and the screen filled all of the left, right, and superior regions of the observer’s visual field, and most of the inferior field. Stimulus edges were presented at two locations on the screen, both at eye-height, using two slide projectors positioned just behind the observer’s shoulders. The observer fixated one projected edge in the middle of the screen, while the other edge was presented 24° to the right of the foveal stimulus. There were two experimental conditions: in the sharp condition, a pattern of broad (6°), sharp-edged, wiggly lines was projected onto the back of the screen using two overhead projectors. The contrast of this pattern was 85%. In the blurry condition, the same pattern was projected but was Gaussian-blurred. The right side of the visual scene, as seen by the observer in the blurry condition, is shown in Fig. 3(B). The edges of the blurred lines in the wiggly-line pattern were measured
with a custom-built microphotometer with an aperture of 1.4 arc min, and were shown to have blur extents of 5°. In both conditions, the scene was produced by two overhead transparencies, and a thick paper border was fixed to each so light from one projector would not impinge on the region of the screen served by the other projector. The patterns cast by the two projectors came together on the screen in a dark vertical line (see the left edge of Fig. 3B), and this seam was positioned approximately 15° to the left of the foveal stimulus field. The luminance of the background images varied between 30 and 300 cd m − 2, and the projector serving the side of the screen carrying the stimuli was angled so that the point of maximum luminance measured from the observer’s eye was half way between the two stimulus fields. In both conditions, two dark patches on the overhead transparencies produced dark squares on the screen subtending 10×10°. These blocking squares were centred on the two 5×5° stimulus fields, so minimal luminance was added to the stimulus regions by the overhead projectors. The borders of the blocking squares were sharp on the screen in the sharp condition, but optically blurred in the blurry condition. The blur extent of the edges of the blocking squares in the blurry condition was 1°.
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Fig. 3(B) Fig. 3. (A) Apparatus for presenting blurred edges in blurry and sharp contexts. Two transparencies carrying the background patterns were projected onto the outside of an upright half-cylinder of drafting paper, 2 m tall and 1 m in diameter. The left (foveal) and right (24° eccentric) stimulus slides were projected over the shoulders of the observer, who sat with the observing eye on the axis of the cylinder. (B) Right side of the screen in Experiment 2 from the point of view of the observer, in the blurred condition. The wavy background pattern was blurred using Adobe Photoshop. The background pattern and the 10× 10° black blocking squares surrounding the stimulus field were then optically blurred. The blurred borders of the 5 ×5° stimulus field were produced by a small square window in the optical path within each slide projector. The observer fixated the centre of the left stimulus field.
The stimuli were slides of computer-generated, horizontal, Gaussian-blurred edges. We used the method of constant stimuli, presenting one of three standard edges in the periphery, with blur extents of 1.2, 1.6, or 2.0°. Each standard was judged against a set of eight foveal comparison blurs. The extents of the
comparison blurs increased in steps of 0.2°, and the range of comparison blurs for each standard blur was centred on that standard. The edges were centred in 5× 5° fields. The foveal and peripheral edges had Michelson contrasts of 0.91 and 0.94, respectively.
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We applied a rectangular window of black duct tape directly to a glass heat shield in the optical path of each slide projector, producing blurred borders for the stimulus fields. These edges had a blur extent of 0.8° on the screen. The borders of the stimulus fields were blurred in this way for both the blurred and sharp conditions. We wanted borders in the immediate vicinity of the test edges to be the same in both conditions as we were interested in the effect of changing the blur content of the global visual scene, and were not attempting to measure local induction effects. Observers performed a two-spatial-interval forcedchoice task. On each trial, one of the three peripheral standards was paired with one of its eight comparison blurs presented foveally, and the observer had to indicate which one was blurrier. The observer was asked to make this judgement on the basis of the apparent blur extent, and not the apparent contrast of the blur. Decision time was not restricted, but was not usually more than 2 s. Responses were recorded by hand by the experimenter, who also advanced the slides. The eight trials for each of the three standards were randomly interleaved in each block. These 24 trials were followed by the presentation of two black slides, then the 24 pairs of slides were presented again in the reverse order. Each observer ran ten of these 48-trial blocks in each condition. The order of the conditions was swapped each session. We constructed a separate 8-point psychometric function for each standard, each datum based on 20 trials. From these we derived a point of subjective equality (PSE) for each standard, that is, the foveal blur that would be judged blurrier or sharper than the standard equally often. Three observers voluntarily participated, aged 23 to 36, all members of the vision group at the University of Otago. SG and EW are mildly myopic, with corrections of less than 2 dioptres. DG is emmetropic. All observations were made with vision corrected to normal. EW was naı¨ve about the aims of the experiment.
Fig. 4 (filled symbols). All observers showed small overconstancy effects for all three standard peripheral blurs, with the exception of SG, whose overconstancy for the 2.0° standard was less than significant in both conditions. The foveal matches for the three standard blurs were not significantly different in the blurry and sharp background conditions for any of the observers. We noticed that the amount of overconstancy measured in this experimental setup was rather less than that obtained using the method of adjustment with blurred edges presented on computer monitors. We thought that one reason for this might be that the positions of the peripheral standard edges were not varied, allowing the observer to use the size of the light region of the stimulus to judge the size of the blur extent, bringing the observer’s PSEs closer to the con-
3.3. Results and discussion Each psychometric function was fit with a logistic distribution function, y =100/(1 +exp (− (x − m)/u)), where y is the percentage of responses ‘foveal sharper than peripheral’, x is the blur extent of the comparison blurs, and u is the slope parameter. The parameter m was taken as our estimate of the PSE, as it defines the point on the stimulus axis which gives the y value as 0.5. The standard error for this parameter was multiplied by 1.96 to give 95% confidence intervals for each PSE. The R 2 values for the fits of logistic functions for all observers had a mean of 0.957, and ranged from 0.902 to 0.997. The PSEs obtained in this way for three observers are plotted against the blur of the peripheral standards in
Fig. 4. Points of subjective equality (PSEs) for three peripheral blurs, presented at 24° eccentricity, in the blurred (round symbols) and sharp (square symbols) conditions, for three observers. The diagonal line in each graph indicates perfect sharpness constancy. Filled symbols show data measured with all the stimulus edges centred in their square fields. For two observers, results are also shown (open symbols) for measurements taken with the positions of the peripheral standard edges jittered over the range 91°. Error bars show 95% confidence intervals.
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stancy line. Observer SG reported that this cue was most distracting for the largest blurs, which might explain why her overconstancy effect decreased with increasing standard blur, rather than increased, as seen in the results from EW and DG, and in the studies reported in Galvin et al. (1997). We jittered the vertical positions of the edges in six steps over9 1°, and repeated the experiment with two observers. Their PSEs are plotted with open symbols in Fig. 4. It can be seen that jittering the position of the edges significantly increased SG’s overconstancy for the two larger standard blurs, producing the familiar pattern of increasing overconstancy with increasing standard blur. Jittering the edge positions produced no significant change in overconstancy in DG, who already showed the expected increase in sharpness overconstancy with blur extent with non-jittered stimuli. Most importantly, both observers continued to show no difference in sharpness overconstancy measured in blurry and sharp contexts. We have proposed that subjective edge sharpening is a high-level effect brought about by our knowledge of typical properties of the visual scene. If this is true, then sharpening might be affected not only by properties of the edge itself, but also by a manipulation of the global visual scene. We made what we thought would be a relevant and radical change, blurring everything in the scene surrounding the edge. This produced no change in the sharpness overconstancy in our observers, so we conclude that the template, if it exists, is not affected by the broad context in which an edge is presented.
4. General discussion We have shown that presenting blurred edges for short durations produces sharpness overconstancy for foveal viewing. Recently, Hammett and Georgeson (1998) measured the apparent sharpness of blurred square waves and also found that apparent sharpness increased with decreasing stimulus duration. We have argued that these findings are consistent with the theory that sharpness overconstancy manifests itself under conditions of poor visibility, as it is these conditions which force us to rely on our knowledge of the world as dominated by sharp luminance transitions. We have claimed that, in general, manipulations that increase blur discrimination thresholds also increase sharpening. An exception to this, which we have noted previously (Hailstone, 1997; Galvin, Squire, Hailstone & O’Shea, 1998b), is that plots of just-noticeable differences (JNDs) in blur against pedestal blur exhibit a dipper shape for small blurs, in both fovea and periphery (Hess, Pointer, & Watt, 1989), but we have found only monotonic increases in blur appearance with increases in real blur in peripheral vision. Dipper-shaped blur threshold functions have been modelled by
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Pa¨a¨kko¨nen and Morgan (1994), who apply Weber’s Law to an internal representation of blur which takes into account the effects of intrinsic blur. This model implies that the internal JNDs in blur increase monotonically with pedestal blur, even for the smallest blurs, and it may be these JNDs to which changes in appearance are related. We agree that the appearance of edges may be affected by intrinsic blur, as we (Galvin et al., 1997) found a slight blurring of sharp edges in peripheral vision which matched estimates of intrinsic blur made by Levi and Klein (1990). There is disagreement in the literature about the nature of the relationship between blur thresholds and blur appearance. Hammett (1997) argued that, in the case of moving, blurred edges, it is the motion sharpening process itself that produces increases in the blur discrimination thresholds. He based this conclusion on the finding that it was blurred edges moving at different (slow) speeds, but with the same apparent extents, that had the same Weber fractions for blur discrimination, rather than blurs that had the same physical extents. Burr and Morgan (1997), on the other hand, proposed that the appearance and discrimination of moving stimuli may be determined by different mechanisms, finding a much larger effect of increasing exposure duration from 40 to 150 ms on the apparent length of the smear tail of moving dots than on blur discrimination thresholds. It is unclear whether a single model will eventually account for the changes in both blur discrimination and blur appearance that occur when visibility is compromised in various ways; existing models of blur discrimination have not attempted to explain the appearance of briefly presented blurs. We rejected a number of low-level explanations for sharpness overconstancy in a previous paper (Galvin et al., 1997) but were impressed by the findings of Hammett and Bex (1996). They showed that sharpening of a drifting sinusoid could be reduced by adapting to stimuli containing higher spatial frequencies than the test stimulus, and suggested that some low-level non-linearity in contrast coding could be generating spatial frequencies higher than that of the test, which would in turn produce a sharper percept. Recently, Hammett, Georgeson and Gorea (1998) have developed this idea into a model which explains the motion sharpening as a result of compressive contrast non-linearities in ganglion cells of the magnocellular pathway (M cells). Fits of their model show that the degree of compression in the non-linearity required to produce their empirical shifts in blur appearance are consistent with those recorded in individual M cells. They argue that both kinds of sharpness overconstancy for static stimuli have been measured in conditions where M cells make a large contribution to perception: the perception of short duration stimuli is mediated by the transient subcortical system, and the peripheral sharpness overconstancy
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effect is accounted for by the higher ratio of M to P cells in the periphery. Although we find the argument that a contrast nonlinearity could produce sharpness overconstancy compelling, we are cautious about assigning this effect to the M pathways. Lennie (1993) and others (e.g. Merigan, Byrne & Maunsell, 1991; Galvin, Williams & Coletta, 1996) have argued that the P cell population can contribute significantly to the representation of transient and moving stimuli. Parvocellular neurons of the lateral geniculate nucleus have a peak temporal sensitivity of 10 Hz in monkeys (Derrington & Lennie, 1984), so we would predict that neurons in the human visual system should prefer a 100 ms stimulus, yet we found significant sharpness overconstancy with a similar duration in Experiment 1. A more specific objection to Hammett’s intriguing suggestion is that if compressive non-linearity in contrast coding by M cells accounted for sharpening in the short duration case, it does not explain why equating for visibility by M-scaling stimulus field sizes in the peripheral study equates overconstancy (Galvin et al., 1997), as changing the field size does not change the ratio of M to P cells. Another explanation for apparent sharpening of blurred edges was offered by Burr and Morgan (1997). They suggested that blur appearance is determined by a default rule that the blur looks like the sharpest blur from which it cannot be distinguished. We have compared the sharpening measured in the current study with the most appropriate available blur discrimination data, those for the 95% contrast, stationary, short-duration bars reported in Burr and Morgan (1997), and find that over most of the range of blurs we have examined (that is, all but the very small ones), the shifts in blur appearance are much larger than the JNDs for the same blurs, so poor blur discrimination does not fully account for the sharpening effect. We have found the same to be true for blurs presented in the periphery, where sharpness overconstancy exceeded blur decrement thresholds for blurs with space constants of 12 to 20 arc min (Hailstone, 1997). We have offered the idea of a sharpness template in the spirit of a Gestalt-like principle which might be derived from Wertheimer’s Law of Pra¨gnanz, which suggests that our perceptions will make good order out of incoming information (Koffka, 1935). We wondered if such a high-level mechanism might be susceptible to a global change in the visual scene, and tried to recalibrate our observers’ assumptions about the nature of typical luminance transitions by measuring blur appearance in a totally blurry context. We found that blurring the current visual context plays no role in defining the default assumption about the blurriness of the world. This may mean that there is no template for sharp edges to be influenced, or it may be that the template is very robust, perhaps yielding only to a prolonged pe-
riod of adaptation to blur. Myopes who are accustomed to enduring a blurry scene for the duration of the occasional search for their spectacles may have been conditioned out of adjusting their edge templates; our observers were emmetropic or near-emmetropic, and showed a similar resistance to any effect of a blurred context on edge appearance.
5. Conclusion Blurred edges presented for durations of less than 1 s undergo sharpening. This new observation complements measurements of peripheral sharpness overconstancy and motion sharpening, providing a third demonstration of sharpness overconstancy in conditions of poor visibility. We have argued that these results are consistent with the idea that our perception of edges is influenced by a template for edges that is sharp. We have found no effect of a completely blurry context on measurements of peripheral sharpness overconstancy, and conclude that if there is a template for edges, it is resistant to contextual influences.
Acknowledgements We would like to thank Donovan Govan, James Dignan, and Carl Beuke for being experimenters, Donovan Govan and Emma Willcock for being observers, and Donovan Govan for programming and scene measurement. We thank Jeff Miller for suggesting Experiment 1. We thank David Burr and an anonymous reviewer for helpful comments on the original manuscript. Some of the data in this study were presented at ICONIP’97 (Galvin et al., 1998b) and the 1998 meeting of the Association for Research in Vision and Ophthalmology (Galvin, Squire, Hailstone, & O’Shea, 1998a).
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